A second-order accurate fluid-in-cell(FLIC) method for the 2D shallow water equations with topography

The fluid-in-cell(FLIC)approach of Gentry et al.(1966)is extended to second-order accuracy in space and applied to solve the 2D shallow water equations with topography.The FLIC method can be interpreted in a finite volume sense,it therefore conserves both water mass and momentum.Like the original FLIC method the second-order FLIC method presented here is able to handle wetting-drying fronts without any special treatment.Moreover,the resulting method is shock capturing and well-balanced,satisfying both the C-and extended C-properties exactly.